0.11/0.12 % Problem : Vampire---4.8_31262 : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : do_cvc5 %s %d 0.12/0.34 % Computer : n008.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Mon Jul 3 12:57:49 EDT 2023 0.12/0.34 % CPUTime : 0.19/0.46 %----Proving TH0 0.19/0.48 thf(in_type,type, 0.19/0.48 in: $i > $i > $o ). 0.19/0.48 0.19/0.48 thf(emptyset_type,type, 0.19/0.48 emptyset: $i ). 0.19/0.48 0.19/0.48 thf(setadjoin_type,type, 0.19/0.48 setadjoin: $i > $i > $i ). 0.19/0.48 0.19/0.48 thf(dsetconstr_type,type, 0.19/0.48 dsetconstr: $i > ( $i > $o ) > $i ). 0.19/0.48 0.19/0.48 thf(subset_type,type, 0.19/0.48 subset: $i > $i > $o ). 0.19/0.48 0.19/0.48 thf(kpair_type,type, 0.19/0.48 kpair: $i > $i > $i ). 0.19/0.48 0.19/0.48 thf(cartprod_type,type, 0.19/0.48 cartprod: $i > $i > $i ). 0.19/0.48 0.19/0.48 thf(singleton_type,type, 0.19/0.48 singleton: $i > $o ). 0.19/0.48 0.19/0.48 thf(singleton,definition, 0.19/0.48 ( singleton 0.19/0.48 = ( ^ [A: $i] : 0.19/0.48 ? [Xx: $i] : 0.19/0.48 ( ( in @ Xx @ A ) 0.19/0.48 & ( A 0.19/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.19/0.48 0.19/0.48 thf(ex1_type,type, 0.19/0.48 ex1: $i > ( $i > $o ) > $o ). 0.19/0.48 0.19/0.48 thf(ex1,definition, 0.19/0.48 ( ex1 0.19/0.48 = ( ^ [A: $i,Xphi: $i > $o] : 0.19/0.48 ( singleton 0.19/0.48 @ ( dsetconstr @ A 0.19/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.19/0.48 0.19/0.48 thf(breln_type,type, 0.19/0.48 breln: $i > $i > $i > $o ). 0.19/0.48 0.19/0.48 thf(breln,definition, 0.19/0.48 ( breln 0.19/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ). 0.19/0.48 0.19/0.48 thf(func_type,type, 0.19/0.48 func: $i > $i > $i > $o ). 0.19/0.48 0.19/0.48 thf(func,definition, 0.19/0.48 ( func 0.19/0.48 = ( ^ [A: $i,B: $i,R: $i] : 0.19/0.48 ( ( breln @ A @ B @ R ) 0.19/0.48 & ! [Xx: $i] : 0.19/0.48 ( ( in @ Xx @ A ) 0.19/0.48 => ( ex1 @ B 0.19/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ). 0.19/0.48 0.19/0.48 thf(ap_type,type, 0.19/0.48 ap: $i > $i > $i > $i > $i ). 0.19/0.48 0.19/0.48 thf(funcGraphProp1_type,type, 0.19/0.48 funcGraphProp1: $o ). 0.19/0.48 0.19/0.48 thf(funcGraphProp1,definition, 0.19/0.48 ( funcGraphProp1 0.19/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.19/0.48 ( ( func @ A @ B @ Xf ) 0.19/0.48 => ! [Xx: $i] : 0.19/0.48 ( ( in @ Xx @ A ) 0.19/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ). 0.19/0.48 0.19/0.48 thf(funcGraphProp2_type,type, 0.19/0.48 funcGraphProp2: $o ). 0.19/0.48 0.19/0.48 thf(funcGraphProp2,definition, 0.19/0.48 ( funcGraphProp2 0.19/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.19/0.48 ( ( func @ A @ B @ Xf ) 0.19/0.48 => ! [Xx: $i] : 0.19/0.48 ( ( in @ Xx @ A ) 0.19/0.48 => ! [Xy: $i] : 0.19/0.48 ( ( in @ Xy @ B ) 0.19/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) 0.19/0.48 => ( ( ap @ A @ B @ Xf @ Xx ) 0.19/0.48 = Xy ) ) ) ) ) ) ) ). 0.19/0.48 0.19/0.48 thf(funcextLem,conjecture, 0.19/0.48 ( funcGraphProp1 0.19/0.48 => ( funcGraphProp2 0.19/0.48 => ! [A: $i,B: $i,Xf: $i] : 0.19/0.48 ( ( func @ A @ B @ Xf ) 0.19/0.48 => ! [Xg: $i] : 0.19/0.48 ( ( ! [Xx: $i] : 0.19/0.48 ( ( ( ap @ A @ B @ Xf @ Xx ) 0.19/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) 0.19/0.48 <= ( in @ Xx @ A ) ) 0.19/0.48 => ! [Xx: $i] : 0.19/0.48 ( ( in @ Xx @ A ) 0.19/0.48 => ! [Xy: $i] : 0.19/0.48 ( ( in @ Xy @ B ) 0.19/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg ) 0.19/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) 0.19/0.48 <= ( func @ A @ B @ Xg ) ) ) ) ) ). 0.19/0.48 0.19/0.48 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.EilWcYfaWd/cvc5---1.0.5_31364.p... 0.19/0.48 (declare-sort $$unsorted 0) 0.19/0.48 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.19/0.48 (declare-fun tptp.emptyset () $$unsorted) 0.19/0.48 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.19/0.48 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.19/0.48 (declare-fun tptp.subset ($$unsorted $$unsorted) Bool) 0.19/0.48 (declare-fun tptp.kpair ($$unsorted $$unsorted) $$unsorted) 0.19/0.48 (declare-fun tptp.cartprod ($$unsorted $$unsorted) $$unsorted) 0.19/0.48 (declare-fun tptp.singleton ($$unsorted) Bool) 0.19/0.48 (assert (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.19/0.48 (declare-fun tptp.ex1 ($$unsorted (-> $$unsorted Bool)) Bool) 0.19/0.48 (assert (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.19/0.48 (declare-fun tptp.breln ($$unsorted $$unsorted $$unsorted) Bool) 0.19/0.48 (assert (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) 0.19/0.48 (declare-fun tptp.func ($$unsorted $$unsorted $$unsorted) Bool) 0.19/0.48 (assert (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) 42.13/42.30 (declare-fun tptp.ap ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted) 42.13/42.30 (declare-fun tptp.funcGraphProp1 () Bool) 42.13/42.30 (assert (= tptp.funcGraphProp1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf))))))) 42.13/42.30 (declare-fun tptp.funcGraphProp2 () Bool) 42.13/42.30 (assert (= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy)))))))))) 42.13/42.30 (assert (not (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 Xg) (@ _let_1 Xf)))))))))))))))) 42.13/42.30 (set-info :filename cvc5---1.0.5_31364) 42.13/42.30 (check-sat-assuming ( true )) 42.13/42.30 ------- get file name : TPTP file name is 42.13/42.30 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31364.smt2... 42.13/42.30 --- Run --ho-elim --full-saturate-quant at 10... 42.13/42.30 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 42.13/42.30 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 42.13/42.30 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 42.13/42.30 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 42.13/42.30 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 42.13/42.30 % SZS status Theorem for 42.13/42.30 % SZS output start Proof for 42.13/42.30 ( 42.13/42.30 (let ((_let_1 (not (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 Xg) (@ _let_1 Xf))))))))))))))))) (let ((_let_2 (= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy))))))))))) (let ((_let_3 (= tptp.funcGraphProp1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))))) (let ((_let_4 (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))))) (let ((_let_5 (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))))) (let ((_let_6 (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) (let ((_let_7 (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) (let ((_let_8 (tptp.kpair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (tptp.in _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.ap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.kpair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_10))) (let ((_let_12 (tptp.in _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (tptp.ap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_13))) (let ((_let_15 (= _let_10 _let_13))) (let ((_let_16 (tptp.in _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (not _let_20))) (let ((_let_22 (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (or (not (@ (@ tptp.in Xx) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (= (@ (@ _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) Xx) (@ (@ _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) Xx))))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1)))))))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.cartprod SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_27 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_26))) (let ((_let_28 (not _let_27))) (let ((_let_29 (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1)))))))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_26))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30 _let_28 _let_25 _let_23 _let_21 _let_19 _let_17 _let_9))) (let ((_let_34 (not _let_9))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_946 $$unsorted) (BOUND_VARIABLE_944 $$unsorted) (BOUND_VARIABLE_942 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_946) BOUND_VARIABLE_944)))) (let ((_let_2 (@ (@ tptp.cartprod A) B))) (or (not (@ (@ tptp.subset Xf) _let_2)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1))))))))) (not (@ (@ tptp.subset BOUND_VARIABLE_942) _let_2)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) BOUND_VARIABLE_942))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1))))))))) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (or (not (@ (@ tptp.in Xx) A)) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 BOUND_VARIABLE_942) Xx)))))) (not (@ (@ tptp.in BOUND_VARIABLE_946) A)) (not (@ (@ tptp.in BOUND_VARIABLE_944) B)) (not (@ _let_1 BOUND_VARIABLE_942)) (@ _let_1 Xf))))))) (let ((_let_36 (not _let_33))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO _let_37 :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (ASSUME :args (_let_5)))) (let ((_let_40 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_39 _let_38 _let_37) :args ((= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_40 _let_39 _let_38 _let_37) :args ((= tptp.funcGraphProp1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_796 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_796) A)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_796) (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_796))) Xf)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_41 _let_40 _let_39 _let_38 _let_37) :args ((= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_853 $$unsorted) (BOUND_VARIABLE_851 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_851) A)) (not (@ (@ tptp.in BOUND_VARIABLE_853) B)) (not (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_851) BOUND_VARIABLE_853)) Xf)) (= BOUND_VARIABLE_853 (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_851))))) SB_DEFAULT SBA_FIXPOINT))) _let_41 _let_40 _let_39 _let_38 _let_37) :args ((not (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_946 $$unsorted) (BOUND_VARIABLE_944 $$unsorted) (BOUND_VARIABLE_942 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_946) BOUND_VARIABLE_944)))) (let ((_let_2 (@ (@ tptp.func A) B))) (or (not (@ _let_2 Xf)) (not (@ _let_2 BOUND_VARIABLE_942)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (or (not (@ (@ tptp.in Xx) A)) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 BOUND_VARIABLE_942) Xx)))))) (not (@ (@ tptp.in BOUND_VARIABLE_946) A)) (not (@ (@ tptp.in BOUND_VARIABLE_944) B)) (not (@ _let_1 BOUND_VARIABLE_942)) (@ _let_1 Xf)))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_43 (NOT_IMPLIES_ELIM2 _let_42))) (let ((_let_44 (or))) (let ((_let_45 (not _let_35))) (let ((_let_46 (=>))) (let ((_let_47 (not))) (let ((_let_48 (@ tptp.in _let_8))) (let ((_let_49 (@))) (let ((_let_50 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_51 (@ tptp.kpair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_52 (REFL :args (tptp.in)))) (let ((_let_53 (CONG _let_52 (THEORY_PREPROCESS :args ((= (@ _let_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_8))) :args _let_49))) (let ((_let_54 (CONG (TRANS (CONG _let_53 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) :args _let_49) (THEORY_PREPROCESS :args ((= (@ _let_48 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_16)))) :args _let_47))) (let ((_let_55 (CONG (THEORY_PREPROCESS :args ((= (@ (@ tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_18))) :args _let_47))) (let ((_let_56 (CONG (THEORY_PREPROCESS :args ((= (@ (@ tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_20))) :args _let_47))) (let ((_let_57 (REFL :args (_let_25)))) (let ((_let_58 (@ tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_59 (THEORY_PREPROCESS :args ((= (@ (@ tptp.cartprod SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_26))))) (let ((_let_60 (CONG (TRANS (CONG (REFL :args (_let_58)) _let_59 :args _let_49) (THEORY_PREPROCESS :args ((= (@ _let_58 _let_26) _let_27)))) :args _let_47))) (let ((_let_61 (REFL :args (_let_30)))) (let ((_let_62 (@ tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_63 (CONG (TRANS (CONG (REFL :args (_let_62)) _let_59 :args _let_49) (THEORY_PREPROCESS :args ((= (@ _let_62 _let_26) _let_31)))) :args _let_47))) (let ((_let_64 (_let_45))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64) (CONG (REFL :args _let_64) (CONG (CONG _let_63 _let_61 _let_60 _let_57 (REFL :args (_let_23)) _let_56 _let_55 _let_54 (TRANS (CONG _let_53 _let_50 :args _let_49) (THEORY_PREPROCESS :args ((= (@ _let_48 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_9)))) :args _let_44) :args _let_47) :args _let_46))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_35))) (REFL :args (_let_36)) :args _let_44)) (NOT_IMPLIES_ELIM2 _let_43) :args (_let_36 true _let_35)))) (let ((_let_66 (or _let_32 _let_30 _let_21 _let_12))) (let ((_let_67 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_796 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_796) A)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_796) (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_796))) Xf))))) (let ((_let_68 (@ (@ tptp.ap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_69 (@ _let_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_70 (THEORY_PREPROCESS :args ((= (@ _let_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_10))))) (let ((_let_71 (_let_67))) (let ((_let_72 (REFL :args (_let_33)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 5)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_44)) :args ((or _let_20 _let_33))) _let_65 :args (_let_20 true _let_33)))) (let ((_let_74 (or _let_28 _let_25 _let_21 _let_19 _let_17 _let_14))) (let ((_let_75 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_853 $$unsorted) (BOUND_VARIABLE_851 $$unsorted)) (or (not (@ (@ tptp.subset Xf) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xx)) Xf))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1))))))))) (not (@ (@ tptp.in BOUND_VARIABLE_851) A)) (not (@ (@ tptp.in BOUND_VARIABLE_853) B)) (not (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_851) BOUND_VARIABLE_853)) Xf)) (= BOUND_VARIABLE_853 (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_851)))))) (let ((_let_76 (=))) (let ((_let_77 (THEORY_PREPROCESS :args ((= (@ (@ _let_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_13))))) (let ((_let_78 (_let_75))) (let ((_let_79 (or _let_21 _let_15))) (let ((_let_80 (_let_22))) (let ((_let_81 (ASSUME :args (_let_34)))) (let ((_let_82 (ASSUME :args (_let_14)))) (let ((_let_83 (ASSUME :args (_let_15)))) (let ((_let_84 (ASSUME :args (_let_12)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_81 _let_82 _let_83 _let_84) :args (_let_34 _let_12 _let_14 _let_15)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_84)) (CONG (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (TRANS (SYMM (SYMM _let_83)) (SYMM _let_82)) :args (APPLY_UF tptp.kpair)) _let_50 :args (APPLY_UF tptp.in)) (FALSE_INTRO _let_81))) :args (_let_34 _let_14 _let_15 _let_12)) :args ((not (and _let_34 _let_12 _let_14 _let_15)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_9))) (REFL :args ((not _let_12))) (REFL :args ((not _let_14))) (REFL :args ((not _let_15))) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_21 _let_15 (not _let_79)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((@ _let_69 Xx)))) :args _let_80) (CONG (REFL :args _let_80) (CONG _let_56 (CONG _let_70 _let_77 :args _let_76) :args _let_44) :args _let_46))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 4)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_44)) :args ((or _let_22 _let_33))) _let_65 :args (_let_22 true _let_33)) :args (_let_79 false _let_22)) :args (_let_15 false _let_20 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_25 _let_17 _let_19 _let_21 _let_28 _let_14 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 3)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_44)) :args ((or _let_24 _let_33))) _let_65 :args (_let_24 true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 7)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_44)) :args ((or _let_16 _let_33))) _let_65 :args (_let_16 true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 6)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_44)) :args ((or _let_18 _let_33))) _let_65 :args (_let_18 true _let_33)) _let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 2)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_44)) :args ((or _let_27 _let_33))) _let_65 :args (_let_27 true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_78) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((@ (@ tptp.cartprod A) B) (@ tptp.subset Xf) (@ (@ tptp.kpair BOUND_VARIABLE_851) BOUND_VARIABLE_853)))) :args _let_78) (CONG (REFL :args _let_78) (CONG _let_60 _let_57 _let_56 _let_55 _let_54 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_77 :args _let_76) :args _let_44) :args _let_46))) (NOT_IMPLIES_ELIM1 _let_43) :args (_let_74 false _let_75)) :args (_let_14 false _let_24 false _let_16 false _let_18 false _let_20 false _let_27 false _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_30 _let_21 _let_32 _let_12 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_44)) :args ((or _let_29 _let_33))) _let_65 :args (_let_29 true _let_33)) _let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_44)) :args ((or _let_31 _let_33))) _let_65 :args (_let_31 true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_71) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((@ tptp.kpair BOUND_VARIABLE_796) (@ (@ (@ tptp.ap A) B) Xf)))) :args _let_71) (CONG (REFL :args _let_71) (CONG _let_63 _let_61 _let_56 (TRANS (CONG (CONG _let_52 (TRANS (CONG (REFL :args (_let_51)) _let_70 :args _let_49) (THEORY_PREPROCESS :args ((= (@ _let_51 _let_10) _let_11)))) :args _let_49) _let_50 :args _let_49) (THEORY_PREPROCESS :args ((= (@ (@ tptp.in _let_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_12)))) :args _let_44) :args _let_46))) (NOT_IMPLIES_ELIM1 _let_42) :args (_let_66 false _let_67)) :args (_let_12 false _let_29 false _let_20 false _let_31 false _let_66)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 8)) _let_65 :args (_let_34 true _let_33)) :args (false false _let_15 false _let_14 false _let_12 true _let_9)) :args (_let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 42.13/42.31 ) 42.13/42.31 % SZS output end Proof for 42.13/42.31 % cvc5---1.0.5 exiting 42.13/42.31 % cvc5---1.0.5 exiting 42.19/42.31 EOF